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Decomposition matrices for spin characters of symmetric groups. (English) Zbl 0651.20007
Let \(\tilde S_ n\) be a double cover of the symmetric group \(S_ n\). The faithful irreducible characters of \(\tilde S_ n\) are called spin characters. In this paper a study of the p-decomposition numbers of such characters is initiated for odd prime integers p. A general technique is developed by a non-trivial modification of a corresponding technique for the characters of \(S_ n\). Then the decomposition numbers are determined explicitly for \(p=3\) and \(3\leq n\leq 11\) with an ambiguity for \(n=9\). The second author will deal separately with the cases \(p=5,7,11\).
Reviewer: J.B.Olsson

MSC:
20C30 Representations of finite symmetric groups
20C20 Modular representations and characters
20C25 Projective representations and multipliers
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